Lecture 5: Two loci, new concepts
- Linkage disequilibrium and its rate of decay
- Hitchhiking
- Modifier analysis
So far we have considered only the case for one locus with two alleles. We can expand the analysis either by
considering more alleles or by considering more loci.
Here we look at what happens when we incorporate another locus.
Let us take the simplest example - two loci, each with two alleles - A and a at one locus and B and b
at a second locus. We must specific frequencies for each gamete type:
Gamete Frequency
AB P
Ab Q
aB R
ab S
From these we can write that:
P+Q+R+S=1
frequency A= P+Q
frequency a= R+S etc
, Note we cannot assume that the frequency of AB type is simply the frequency of the A allele x frequency of B.
p(AB)= p(A) x p(B) – linkage equilibrium (no coupling of alleles)
It could be the case, for example, that whenever one finds A one also finds B ie Ab doesn't exist. In which case
the frequency of AB is actually higher than the frequency of A x freq B. Likewise freq ab must be higher than
the frequency of a x freq b. Such a population would be said to be in linkage disequilibrium – the non-
random association of alleles at different loci. We can again be more precise. We can write that
P=probability of A x probablity of B + D where D is the linkage
disequilibrium.
p(AB) = p(A) x p(B) + D
Likewise
Q=probability of A x probablity of b - D = p(A) x p(b) - D
R=probability of a x probablity of B - D = p(a) x p(B) - D
S=probability of a x probablity of b +D = P(a) x p(b) + D
D is our measure of Linkage disequilibrium: to see this better, consider going shopping. You can buy:
Apples (A) or oranges (a)
Beer (B) or wine (b)
If people who like beer over wine are no more or less likely to prefer apples over oranges
Then:
p(Apples and Beer)=p(A) x p(B)
- Linkage disequilibrium and its rate of decay
- Hitchhiking
- Modifier analysis
So far we have considered only the case for one locus with two alleles. We can expand the analysis either by
considering more alleles or by considering more loci.
Here we look at what happens when we incorporate another locus.
Let us take the simplest example - two loci, each with two alleles - A and a at one locus and B and b
at a second locus. We must specific frequencies for each gamete type:
Gamete Frequency
AB P
Ab Q
aB R
ab S
From these we can write that:
P+Q+R+S=1
frequency A= P+Q
frequency a= R+S etc
, Note we cannot assume that the frequency of AB type is simply the frequency of the A allele x frequency of B.
p(AB)= p(A) x p(B) – linkage equilibrium (no coupling of alleles)
It could be the case, for example, that whenever one finds A one also finds B ie Ab doesn't exist. In which case
the frequency of AB is actually higher than the frequency of A x freq B. Likewise freq ab must be higher than
the frequency of a x freq b. Such a population would be said to be in linkage disequilibrium – the non-
random association of alleles at different loci. We can again be more precise. We can write that
P=probability of A x probablity of B + D where D is the linkage
disequilibrium.
p(AB) = p(A) x p(B) + D
Likewise
Q=probability of A x probablity of b - D = p(A) x p(b) - D
R=probability of a x probablity of B - D = p(a) x p(B) - D
S=probability of a x probablity of b +D = P(a) x p(b) + D
D is our measure of Linkage disequilibrium: to see this better, consider going shopping. You can buy:
Apples (A) or oranges (a)
Beer (B) or wine (b)
If people who like beer over wine are no more or less likely to prefer apples over oranges
Then:
p(Apples and Beer)=p(A) x p(B)
